Multimode directionality in all-dielectric metasurfaces

We demonstrate that spectrally diverse multiple magnetic dipole resonances can be excited in all-dielectric structures lacking rotational symmetry, in contrast to conventionally used spheres, disks, or spheroids. Such multiple magnetic resonances arise from hybrid Mie-Fabry-Perot modes, and can constructively interfere with induced electric dipole moments, thereby leading to novel multifrequency unidirectional scattering. Here we focus on elongated dielectric nanobars, whose magnetic resonances can be spectrally tuned by their aspect ratios. Based on our theoretical results, we suggest all-dielectric multimode metasurfaces and verify them in proof-of-principle microwave experiments. We also believe that the demonstrated property of multimode directionality is largely responsible for the best efficiency of all-dielectric metasurfaces that were recently shown to operate across multiple telecom bands.

Figure 1

Classes of all-dielectric meta-atoms: (a) Sphere and nanodisk with high refractive index described by the three-dimensional Mie scattering theory. Characteristic dimensions ($d$ and $L$) are much smaller than the free-space wavelength $\lambda$. (b) Finite-size nanorod ($L\sim \lambda$) with a high aspect ratio supporting the hybrid Mie-Fabry-Perot as described in this work. (c) Long nanorod ($L\gg \lambda$) described by the two-dimensional Mie scattering theory.

Figure 2

(a), (b) Schematic diagrams of (a) an elongated ($W=110$ nm, $L_y=400$ nm, and $L_z=220$ nm) and (b) a symmetric ($W=L=400$ nm) silicon nanobar. (c), (d) Simulated scattering spectra (solid black line) and calculated multipole decompositions (total contributions: dotted red line, ED: dotted blue line, MD: dotted green line, EQ: dotted magenta line) of (c) the elongated and (d) symmetric nanobar, respectively.

Figure 3

(a), (c) Near-field distributions in the middle cut plane ($z=0$) and 3D far-field scattering patterns of the nanobar at (a) $\lambda =992$ nm and (c) $\lambda =721$ nm, respectively. The colors represent normalized amplitudes of the electric and magnetic fields, and arrows show the field vectors. (b), (d) Simulated far-field scattering patterns (dotted black line) and calculated multipole radiation patterns (solid red line) at (b) $\lambda =992$ nm and (d) $\lambda =721$ nm, respectively. The patterns are normalized to the maximum scattering intensity in the far field.

Figure 4

Scattering efficiency spectra as a function of geometric parameters (a) $L_y$ with fixed $W=110$ nm and $L_z=220$ nm, and (b) $W$ with fixed $L_z=220$ nm and $L_y=400$ nm. (c), (d) Scattering spectrum for a nanobar with dimensions marked by the dashed lines in (a) and (b) correspondingly. The insets show the far-field unidirectional scattering patterns at different resonance wavelengths.

Figure 5

(a), (b) Reflection and transmission spectra of the metasurface composed of the silicon nanobars shown in Fig. 2. The periodicities in $x$ and $y$ directions are 160 and 500 nm, respectively. Insets diagram the configuration and corresponding near-field magnetic distributions in the $xy$ plane at ${\mathrm{R}}_1, {\mathrm{T}}_1$, and ${\mathrm{T}}_2$ peak wavelengths. (c) Calculated impedance of the metasurface. The solid black line is the real value $Z^{\prime }$ of the impedance $Z$, which corresponds predominantly to radiation resistance. The green dotted line is the impedance phase. The blue dashed line indicates the impedance-matching condition $Z^{\prime }=Z_0$. (d) Effective permittivity (blue) and permeability (red) of the metasurface obtained using $S$-parameter retrieval. ${\epsilon }^{\prime }$ and ${\mu }^{\prime }$ denote the real parts of $\epsilon$ and $\mu$.

Figure 6

(a) Dielectric bar scatter. Left: A sketch of the experimental setup to measure the radiation pattern of the single scatter with the dimensions $W=0.5$ cm, $L_y=1.8$ cm, and $L_z=1.5$ cm. Right: Experimentally measured (red dots) and CST numerically simulated (solid curves) radiation patterns for the Kerker conditions. (b) Dielectric metasurface. Left: photograph of the fabricated multimode Huygens' metasurface composed of silicon dielectric bars with the dimensions $W=0.5$ cm, $L_y=1.8$ cm, and $L_z=1.5$ cm placed with the periods $P_x=0.9$ cm and $P_y=2.7$ cm. Right: Experimentally measured (solid curves) and CST numerically simulated (dashed curves) reflection and transmission spectra magnitudes of the multimode Huygens' metasurface.

Figure 7

Profile of the resonant cavity modes. Typical TM modes of the rectilinear cavity with quantum numbers (a) $n=1,m=0,l=1$; (b) $n=3,m=0,l=1$; (c) $n=4,m=0,l=1$; and (d) $n=3,m=0,l=2$. The blue arrows indicate electric vector field and the red arrows indicate magnetic vector field. The ${\mathrm{TM}}_{101}$ and ${\mathrm{TM}}_{301}$ modes replicate the field distribution of two magnetic dipole modes in Fig. 3 in the main text.

Figure 8

Equivalent model for second magnetic resonance.

Figure 9

Near-field distributions of electric and magnetic fields of the nanobar with $L_y=1000$ nm, $W=110$ nm, and $L_z=220$ nm.

Figure 10

Near-field distributions of electric and magnetic fields of the nanobar with $W=300$ nm, $L_y=400$ nm, and $L_z=220$ nm.